Hey there, welcome!
Be sure to check out Mohican State Park. Not too far south. Hocking Hills is also a great area. We've also enjoyed Salt Fork and Alum Creek State parks.
Think about the kind of activities you are interested in (horseback riding, boating, hiking, and do some searching.) Lucky us here in Ohio, there are quite a few good options close by.
Somebody else already said: Search these boards, there is a section dedicated to parks and attractions as well as roads and routes for longer trips.